Digital Geometry in Image Processing

Exploring theories and applications developed during the last 30 years, Digital Geometry in Image Processing presents a mathematical treatment of the properties of digital metric spaces and their relevance in analyzing shapes in two and three dimensions. Unlike similar books, this one connects the two areas of image processing and digital geometry, highlighting important results of digital geometry that are currently used in image analysis and processing.

The book discusses different digital geometries in multi-dimensional integral coordinate spaces. It also describes interesting properties of the geometries, including metric and topological properties, shapes of circles and spheres, proximity to Euclidean norms, and number theoretic representations of geometric objects such as straight lines and circles. The authors--all active researchers in image processing and digital geometry--demonstrate how these concepts and properties are useful in various techniques for image processing and analysis. In particular, the book covers applications in object representation and shape analysis.

With many figures (some in color) and end-of-chapter exercises, this book provides an in-depth, unified account of digital metrics, the characterization of digital curves and straight lines, and their uses in shape analysis. It gives you insight on the latest two- and three-dimensional image processing applications.

《數位幾何在影像處理中的應用》探索了過去30年間發展的理論和應用，提供了對數位度量空間的性質及其在二維和三維形狀分析中的相關性的數學處理。與類似的書籍不同，本書將影像處理和數位幾何兩個領域聯繫起來，突出了目前在影像分析和處理中使用的數位幾何重要結果。

本書討論了多維積分坐標空間中的不同數位幾何，並描述了幾何的有趣性質，包括度量和拓撲性質、圓和球的形狀、與歐幾里得範數的接近程度，以及幾何物體（如直線和圓）的數論表示。作為影像處理和數位幾何領域的活躍研究者，作者們展示了這些概念和性質在影像處理和分析的各種技術中的用途。特別是，本書涵蓋了物體表示和形狀分析的應用。

本書配有許多圖片（其中一些是彩色的）和章末練習題，提供了對數位度量、數位曲線和直線的特徵以及它們在形狀分析中的應用的深入統一介紹。它讓您深入了解最新的二維和三維影像處理應用。

Jayanta Mukhopadhyay is a professor in the Department of Computer Science and Engineering at the Indian Institute of Technology (IIT) Kharagpur, where he is currently head of the Department of Computer Science and Engineering and the School of Information and Technology. Dr. Mukhopadhyay was a Humboldt Research Fellow at the Technical University of Munich and has held visiting positions at the University of California-Santa Barbara, University of Southern California, and the National University of Singapore. He is a senior member of the IEEE and a fellow of the Indian National Academy of Engineering (INAE). His research interests include image processing, pattern recognition, computer graphics, multimedia systems, and medical informatics. He has published more than 170 journal articles and conference proceedings in these areas. He received his B.Tech., M.Tech., and Ph.D. in electronics and electrical communication engineering from IIT Kharagpur.

Partha Pratim Das is a professor in the Department of Computer Science and Engineering at IIT Kharagpur. He is also a visiting professor in the Institute of Radio Physics and Electronics at Calcutta University. Dr. Das is a member of the Association for Computing Machinery (ACM) and the VLSI Society of India and a reviewer for ACM Computing Surveys and Pattern Recognition Letters. He has published over 40 technical papers in digital geometry, image processing, parallel computing, and knowledge-based systems and has co-authored a book Digital Geometry in Image Processing. His research interests include object tracking and interpretation in videos, medical information processing, and debugging automation for multi-threaded programs. He obtained his B.Tech., M.Tech., and Ph.D. in electronics and electrical communication from IIT Kharagpur.

Samiran Chattopadhyay is a professor in the Department of Information Technology at Jadavpur Univers

Jayanta Mukhopadhyay是印度理工學院（IIT）卡拉格普爾分校計算機科學與工程系的教授，目前擔任計算機科學與工程系和資訊與技術學院的系主任。Mukhopadhyay博士曾在慕尼黑工業大學擔任洪堡研究員，並在加州大學聖塔芭芭拉分校、南加州大學和新加坡國立大學擔任訪問學者。他是IEEE的高級會員，也是印度國家工程學院（INAE）的院士。他的研究興趣包括影像處理、模式識別、計算機圖形學、多媒體系統和醫學信息學。他在這些領域發表了超過170篇期刊文章和會議論文。他在印度理工學院卡拉格普爾分校獲得了電子與電信工程的學士、碩士和博士學位。

Partha Pratim Das是印度理工學院卡拉格普爾分校計算機科學與工程系的教授，也是加爾各答大學無線電物理與電子學研究所的客座教授。Das博士是計算機機械學會（ACM）和印度VLSI學會的成員，也是《ACM Computing Surveys》和《Pattern Recognition Letters》的審稿人。他在數字幾何、影像處理、並行計算和基於知識的系統等領域發表了40多篇技術論文，並合著了一本名為《數字幾何在影像處理中的應用》的書籍。他的研究興趣包括視頻中的物體跟踪和解釋、醫學信息處理以及多線程程序的調試自動化。他在印度理工學院卡拉格普爾分校獲得了電子與電信工程的學士、碩士和博士學位。

Samiran Chattopadhyay是加達夫普爾大學資訊技術系的教授。